/*
 * File: ghanoi.cpp
 * ----------------
 * This file implements the graphical Hanoi functions.
 */

#include <iostream>
#include <string>
#include <memory> // For auto_ptr
#include "error.h"
#include "ghanoi.h"
#include "gobjects.h"
#include "gwindow.h"
#include "stack.h"
using namespace std;

/******** Constants ********/

/* Maximum permitted disks. */
const int kMaxDisks = 8;

/* Size of the window. */
const double kWindowWidth  = 500;
const double kWindowHeight = 300;

/* Number of spindles. */
const int kNumSpindles = 3;

/* Width of one spindle. */
const int kSpindleWidth = 20;

/* Pixel margin between spindle work areas. */
const double kSpindleMarginSize = 10;

/* Smallest possible disk width. */
const double kMinDiskWidth = 3 * kSpindleWidth;

/* Spindle color: Russet! */
const string kSpindleColor = "#80461B";

/* Colors for each disk. */
const string kDiskColors[] = {
   "Red",
   "Yellow",
   "Green",
   "Cyan",
   "Blue",
   "Magenta",
   "Orange",
   "Gray"
};
/* Border colors for each disk.  These are just darker versions of the disk colors
 * given above.
 */
const string kDiskBorderColors[] = {
   "#800000",
   "#808000",
   "#008000",
   "#008080",
   "#000080",
   "#800080",
   "#804000",
   "#404040"
};

/* Default pause time. */
const double kPauseTime = 500;

/* Number of steps in the animation. */
const int kNumAnimationSteps = 50;

struct Spindle {
	/* Which GRects are here right now. */
	Stack<GRect*> disksHere;
	
	/* The rectangle for this spindle. */
	GRect* rect;
	
	/* The start and end x coordinates of the area allocated
	 * to this spindle.  This is the space where disks can be
	 * moved.
	 */
	double startX, endX;
	
	/* The center line for the spindle. */
	double centerX;
};

static struct HanoiGraphics {
	auto_ptr<GWindow> window;
	Vector<Spindle> spindles;
	
	int numDisks;
	double diskHeight;
} hg;

/******** Function Prototypes ********/

void setupSpindles();
void setupDisks();
double diskYPosition(int spindle);

/******** Implementations ********/

/* Initializes the display. */
void initHanoiDisplay(int numDisks) {
	/* Validate input. */
	if (numDisks > kMaxDisks) {
		error("Sorry, but we can't support that many disks.");
	}
	
	if (numDisks <= 0) {
		error("Sorry, but we need a positive number of disks.");
	}

	/* Create a new window to work with. */
	hg.window.reset(new GWindow(kWindowWidth, kWindowHeight));
	hg.window->setWindowTitle("Towers of Hanoi");
	
	/* Determine the height of a single disk.  We want to size the disks such that
	 * each spindle can have all the disks on top of it, then some vertical space to
	 * show the top of each spindle, then two blank spaces above it.  This works
	 * out to needing a number of "virtual disks" equal to the total number of disks
	 * actually used, plus four extras.
	 */
	int numVirtualDisks = numDisks + 4;
	hg.diskHeight = hg.window->getHeight() / numVirtualDisks;
	hg.numDisks = numDisks;
	
	/* Initialize the spindles and disks. */
	setupSpindles();
	setupDisks();	
	
	/* To let people see the setup, pause for a second before returning. */
	pause(kPauseTime);
}

/* Sets up the spindles. */
void setupSpindles() {
	/* Calculate the total horizontal area that can be allocated to a spindle. */
	double workspaceWidth = hg.window->getWidth() / kNumSpindles;
	
	for (int i = 0; i < kNumSpindles; i++) {
		Spindle spindle;
		
		/* Set the work area appropriately. */
		spindle.startX = workspaceWidth * i       + kSpindleMarginSize;
		spindle.endX   = workspaceWidth * (i + 1) - kSpindleMarginSize;
		
		/* Create a rectangle for this spindle.  The spindle will be centered in
		 * the work area and will have height equal to the number of disks plus
		 * one (so the spindle is still visible).  It will also be bottom-aligned.
		 */
		double height = (hg.numDisks + 1) * hg.diskHeight;
		double y = hg.window->getHeight() - height;
		
		/* Determine where the center line is, then center the rectangle around that. */
		spindle.centerX = (spindle.startX + spindle.endX) / 2.0;
		spindle.rect = new GRect(spindle.centerX - kSpindleWidth / 2.0, y, kSpindleWidth, height);
		spindle.rect->setFilled(true);
		spindle.rect->setColor(kSpindleColor);
		
		/* Add that to the display. */
		hg.window->add(spindle.rect);
		
		/* Add this spindle to the list. */
		hg.spindles += spindle;
	}
}

/* Creates and sets up all of the disks that will be used in the simulation. */
void setupDisks() {
	for (int i = 0; i < hg.numDisks; i++) {
		/* We need to determine the position, color, and size of the disk.
		 *
		 * To size the disk, we will linearly interpolate between the workspace
		 * area (the maximum possible width) and the minimum possible disk width
		 * (specified as a constant).  In particular, we want the bottom disk to
		 * have a size that perfectly fills the spindle workspace, and we want
		 * the top disk to have size equal to kMinDiskWidth.  The formula we
		 * will use for this is the following:
		 *
		 * Width of disk 0     = Workspace width.
		 * Width of disk i - 1 = kMinDiskWidth.
		 *
		 * Therefore:
		 *
		 * width = ((kMinDiskWidth - workspaceWidth) / (numDisks - 1)) * i + workspaceWidth
		 *
		 * There is an edge case here when numDisks = 1, so we will special-case it.
		 */
		double workspaceWidth = hg.spindles[0].endX - hg.spindles[0].startX;
		 
		double width;
		if (hg.numDisks == 1) {
			width = workspaceWidth;
		} else {
			width = ((kMinDiskWidth - workspaceWidth) / (hg.numDisks - 1)) * i + workspaceWidth;
		}
		
		/* Given the width, the x coordinate can be found by taking the center line of
		 * the spindle and backing off by half the width.
		 */
		double x = hg.spindles[0].centerX - width / 2.0;
		
		/* We can determine the y coordinate of the disk by using our existing function
		 * for determining where the next disk should go on a spindle.
		 */
		double y = diskYPosition(0);
		
		/* Create the rectangle. */
		GRect* disk = new GRect(x, y, width, hg.diskHeight);
		disk->setColor(kDiskBorderColors[i]);
		disk->setFilled(true);
		disk->setFillColor(kDiskColors[i]);
		
		/* Draw the disk. */
		hg.window->add(disk);
		
		/* Add the disk to the spindle. */
		hg.spindles[0].disksHere.push(disk);
	}	
}

/* Given a spindle number, returns the y coordinate where the next disk
 * would be placed on top of that spindle.
 */
double diskYPosition(int spindle) {
	if (spindle < 0 || spindle >= hg.spindles.size()) {
		error("Invalid spindle number.");
	}
	
	/* The position is determined as follows:
	 *
	 * 1. Start at the bottom of the window.
	 * 2. Back off by the number of disks in the stack.
	 * 3. Back off once more, since we need to give the upper y coordinate.
	 *
	 * This works out to windowHeight - (disksInStack + 1) * diskHeight.
	 */
	return hg.window->getHeight() - (hg.spindles[spindle].disksHere.size() + 1) * hg.diskHeight;
}

/* Given a character, maps that character to a spindle number. */
int charToSpindle(char ch) {
	switch (ch) {
		case 'A': case 'a': return 0;
		case 'B': case 'b': return 1;
        case 'C': case 'c': return 2;
	}
    error("Unknown spindle.");
    return 0;
}

/* Given a time through the animation, represented by a number between 0 (start)
 * and 1 (end), interpolates where along the trajectory the disk would be at that
 * time using a cubic Hermitian spline.  This makes the animation look significantly
 * smoother than before.
 *
 * http://en.wikipedia.org/wiki/Cubic_Hermite_spline
 */
double interpolate(double t) {
	return -2 * t * t * t + 3 * t * t;
}

/* Animates a disk moving from its current position to the destination. */
void animateDiskPath(GRect* disk, double endX, double endY, double totalTime) {
	const double startX = disk->getX(), startY = disk->getY();
	
	/* Animate the motion! */
	for (int i = 0; i < kNumAnimationSteps; i++) {
		/* Interpolate between the start and end positions.  To determine
		 * how much to interpolate, we use a cubic Hermite spline to map
		 * from the fraction of the animation completed to a smoother
		 * animation point.
		 */
		double x = startX + (endX - startX) * interpolate(double(i) / (kNumAnimationSteps - 1));
		double y = startY + (endY - startY) * interpolate(double(i) / (kNumAnimationSteps - 1));
		disk->setLocation(x, y);
		
		/* Pause to let the animation progress.  This will not work out to pausing
		 * for exactly the right amount of time because there's some latency involved
		 * in the graphics calls, but it's "close enough."
		 */
		pause(totalTime / kNumAnimationSteps);
	}
}

/* Animates a single disk moving from one spindle to another. */
void moveSingleDisk(char startCh, char finishCh) {
	/* Convert the start and end spindles to indices. */
	int start = charToSpindle(startCh), end = charToSpindle(finishCh);
	
	/* Confirm that the start spindle isn't empty. */
	if (hg.spindles[start].disksHere.isEmpty()) {
		error("No disks at the start spindle.");
	}
	
	/* Get the disk to move. */
	GRect* disk = hg.spindles[start].disksHere.pop();
	
	/* Make sure we can legally move the disk from the start spindle to the
	 * end spindle.  This uses the size of the GRects as a proxy for the
	 * size of the disk, which is probably not the best idea.  A better
	 * implementation would use a struct to store both the GRect and its
	 * logical size.
	 */
	if (!hg.spindles[end].disksHere.isEmpty() &&
	    hg.spindles[end].disksHere.top()->getWidth() < disk->getWidth()) {
		error("Cannot move a larger disk atop a smaller one.");   
	}
	
	/* Determine how long the animation must take for each of the three parts of the
	 * animation.
	 */
	double eachAnimationTime = kPauseTime / 3;
		
	/* Move the disk up. */
	animateDiskPath(disk, disk->getX(), 0, eachAnimationTime);
	
	/* Move the disk over.  We need to compute the new x coordinate by centering
	 * the disk over the new midline.
	 */
	double newX = hg.spindles[end].centerX - disk->getWidth() / 2.0;
	animateDiskPath(disk, newX, 0, eachAnimationTime);
	
	/* Move the disk down. */
	animateDiskPath(disk, disk->getX(), diskYPosition(end), eachAnimationTime);
	
	/* Update internal state: make sure that the disk is now on the destination
	 * spindle.
	 */
	hg.spindles[end].disksHere.push(disk);
}